Biochemical reactions apparent equilibrium constant

Whenever reporting equilibrium constants, detailed information concerning the reaction conditions should always be indicated. Alberty has also presented an important review of biochemical thermodynamics in which he discusses the apparent equilibrium constant for biochemical reactions (K ) in terms of sums of reactant species. 

This introductory chapter describes the thermodynamics of biochemical reactions in terms of equilibrium constants and apparent equilibrium constants and avoids references to other thermodynamic properties, which are introduced later. 

Equation 4.1-18 can be used to derive the expression for the apparent equilibrium constant K for a biochemical reaction at a specified pH. If a single biochemical reaction is catalyzed, the amounts n of the pseudoisomer groups at each stage of the reaction are given by... 

K and went on to calculate A,G ° and AfH ° at pH 7 and ionic strength 0.25 M for the corresponding reactants. This made it possible to calculate apparent equilibrium constants for six biochemical reactions at 283.15 and... 

When equcalcrx[nt,lnkr,no] is applied to a system of R independent chemical reactions, it requires a R x N transposed stoichiometric number matrix nt, a vector of natural logarithms of the equilibrium constants of independent reactions, and a vector no of the initial concentrations. It can be used at a specified pH by using a R x N transposed stoichiometric number matrix nt, a vector lnkr of natural logarithms of the apparent equilibrium constants of independent biochemical reactions, and a vector no of the initial concentrations. 

When a biochemical half-reaction involves the production or consumption of hydrogen ions, the electrode potential depends on the pH. When reactants are weak acids or bases, the pH dependence may be complicated, but this dependence can be calculated if the pKs of both the oxidized and reduced reactants are known. Standard apparent reduction potentials E ° have been determined for a number of oxidation-reduction reactions of biochemical interest at various pH values, but the E ° values for many more biochemical reactions can be calculated from ArG ° values of reactants from the measured apparent equilibrium constants K. Some biochemical redox reactions can be studied potentiometrically, but often reversibility cannot be obtained. Therefore a great deal of the information on reduction potentials in this chapter has come from measurements of apparent equilibrium constants. 

Since tables of standard apparent reduction potentials and standard transformed Gibbs energies of formation contain the same basic information, there is a question as to whether this chapter is really needed. However, the consideration of standard apparent reduction potentials provides a more global view of the driving forces in redox reactions. There are two contributions to the apparent equilibrium constant for a biochemical redox reaction, namely the standard apparent reduction potentials of the two half-reactions. Therefore it is of interest to compare the standard apparent reduction potentials of various half reactions. 

The apparent equilibrium constant for a biochemical reaction (like equation 9.1-1) at specified pH can be calculated using... 

Source With permission from R. A. Alberty, Arch. Biochem. Biophys. 389, 94-109 (2001). Copyright Academic Press. Note All of these species arc in aqueous solution, but the formal electron e" is not. The convention is that AfG °(e ) = 0. The first two reactions and the last four reactions are whole reactions in contrast with the half-reactions. For the whole reactions the values given here can be used to calculate the apparent equilibrium constants under these conditions. 

The determination of standard transformed enthalpies of biochemical reactions at specified pH, either from temperature coefficients of apparent equilibrium constants or by calorimetric measurements, makes it possible to calculate the corresponding standard transformed entropy of reaction using... 

Calorimetric measurements yield enthalpy changes directly, and they also yield information on heat capacities, as indicated by equation 10.4-1. Heat capacity calorimeters can be used to determine Cj , directly. It is almost impossible to determine ArCp° from measurements of apparent equilibrium constants of biochemical reactions because the second derivative of In K is required. Data on heat capacities of species in dilute aqueous solutions is quite limited, although the NBS Tables give this information for most of their entries. Goldberg and Tewari (1989) have summarized some of the literature on molar heat capacities of species of biochemical interest in their survey on carbohydrates and their monophosphates. Table 10.1 give some standard molar heat capacities at 298.15 K and their uncertainties. The changes in heat capacities in some chemical reactions are given in Table 10.2. 

R. A. Alberty and A. Cornish-Bowden, On the pH dependence of the apparent equilibrium constant K of a biochemical reaction, Trends Biochem. Sci. 18, 288 291 (1993). 

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